A multi-scale analytical canopy (MAC) reflectance model based on the angular second order gap size distribution

Anisotropy in direction hemispherical reflectance of vegetation canopies has been exploited both as a source of information regarding canopy structure and has been considered a source of noise. Geometric optics canopy reflectance models have had some success in relating canopy structure to observed top-of-canopy anisotropy, especially within wavelengths where multiple scattering is not important. However, these models are often scale specific. Furthermore, most models use simplified methods for treating the "hotspot effect" where both the view and illumination direction vectors from a point in the canopy pass through the same gap in the vegetation. We present a multi-scale analytical canopy (MAC) model that deals with an arbitrary number of scales of canopy organisation. The angular gap size distribution defined as the probability of a gap of length λ along the plane containing both view and illumination direction vectors is applied to describe the extent of the "hotspot" effect in a manner that includes all scales. Validation of the MAC model is presented over boreal stands in terms of both top-of-canopy BRDFs as well as sub-canopy gap size distribution. The possibility of using high-resolution imagery to characterize crown clumping using second order reflectance distributions is discussed.